Structures and Energetics of Some Silicon−Phosphorus Compounds

8444

J. Am. Chem. Soc. 1996, 118, 8444-8451

Structures and Energetics of Some Silicon-Phosphorus Compounds: SiHmPHn, SiHmPHnSiHo, and (SiH3)3P. An ab Initio Molecular Orbital Study Anwar G. Baboul and H. Bernhard Schlegel* Contribution from the Department of Chemistry, Wayne State UniVersity, Detroit, Michigan 48202-3489 ReceiVed March 11, 1996. ReVised Manuscript ReceiVed June 21, 1996X

Abstract: The geometries of 48 isomers of SiHmPHn (m + n ) 0-5), SiHmPHnSiHo (m + n + o ) 0-7), and (SiH3)3P have been optimized at the MP2/6-31G(d) level of theory. Silylenes and cyclic structures dominate the compounds with low numbers of hydrogens; nevertheless, there are several examples of silicon-phosphorus multiple bonding. Relative energies, heats of formation, and bond dissociation energies have been calculated at the G2 level of theory. Two empirical schemes have been constructed to fit the atomization energies. A simple bond additivity approach reproduces the data with a mean absolute deviation of 5.3 kcal/mol. Better results are obtained with a group additivity scheme which gives a mean absolute deviation of 3.4 kcal/mol.

Introduction Compared to other aspects of silicon chemistry, surprisingly little is known about the chemistry of SiP bonds. A number of interesting examples of SiP bonding and reactivity can be found in inorganic, organic, and organometallic chemistry.1 Siliconphosphorus bonding is also relevant to chemical vapor deposition of phosphorus-doped silicon for semiconductors.2 With this ab initio molecular orbital study, we hope to contribute to the understanding of the structure and energetics of some simple silicon-phosphorus compounds. Of the parent single-bonded silicon-phosphorus species, silylphosphine has been studied by microwave spectroscopy3 and photoelectron spectroscopy;4 trisilylphosphine has been examined by electron diffraction5 and X-ray crystallography.6 The structures of about 200 SiP compounds have been determined by X-ray crystallography.7 A few of the more interesting ones include Si-P analogues of cyclobutane,8 bicyclobutane,9 spiropentane,10 hexane,11 norbornane,12 adamantane,13 and cuX Abstract published in AdVance ACS Abstracts, August 1, 1996. (1) Armitage, D. A. In The Silicon-Heteroatom Bond; Patai, S., Rappoport, Z., Eds.; J. Wiley: New York, 1989, p 151; 1991, p 183. (2) Jasinski, J. M.; Meyerson, B. S.; Scott, B. A. Annu. ReV. Phys. Chem. 1987, 38, 109. (3) Varma, R.; Ramaprasad, K. R.; Nelson, J. F. J. Chem. Phys. 1975, 63, 915. (4) Cradock, S.; Ebsworth, E. A. V.; Savage, W. J.; Whiteford, R. A. J. Chem. Soc. Faraday Trans. 2 1972, 68, 934. (5) Beagley, B.; Robiette, A. G.; Sheldrick, G. M. J. Chem. Soc. A 1968, 3002. (6) Blake, A. J.; Ebsworth, E. A.; Henderson, S. G. D. Acta Crystallogr. 1991, C47, 486. (7) Cambridge crystal structure database: Allen, F. H.; Davies, J. E.; Galloy, J. J.; Johnson, O.; Kennard, O.; Macrae, C. F.; Mitchell, E. M.; Mitchell, G. F.; Smith, J. M.; Watson, D. G. J. Chem. Inf. Comput. Sci. 1991, 31, 187. (8) Clegg, W.; Haase, M.; Klingebiel, U. K.; Sherldrick, G. M. Chem. Ber. 1983, 116, 146. (9) Driess, M.; Pritzkow, H.; Reisgys, M. Chem. Ber. 1991, 124, 1923. (10) Tebbe, K.-F.; Heinlein, T. Z. Anorg. Allg. Chem. 1984, 515, 7. (11) Driess, M.; Reisgys, M.; Pritzkow, H. Angew. Chem., Int. Ed. Engl. 1992, 31, 1510. (12) Honle, W.; von Schnering, H. G. Z. Anorg. Allg. Chem. 1978, 442, 107. (13) Honle, W.; von Schnering, H. G. Z. Anorg. Allg. Chem. 1978, 442, 91. Baudler, M.; Oehlert, W.; Tebbe, K.-F. Z. Anorg. Allg. Chem. 1991, 598, 9.

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bane.14 Some of these, along with simpler silylphosphines, have found uses as ligands in transition metal complexes.1,7 Siliconphosphorus single bonds are remarkably reactive.1 They react readily with water, oxygen, carbon dioxide, halogens, halides, etc. However, there appears to be no systematic study of the experimental thermochemistry of silicon-phosphorus compounds.15 Far less is known about SidP double bonds.16 Thermal decomposition of substituted 2-silaphosphetane is thought to give an SidP intermediate which dimerizes rapidly.17 Bulky groups stabilize the double bond, making it possible to characterize these compounds spectroscopically and to study their reactivity.18 This approach has recently culminated in the first X-ray crystal structures of compounds containing SidP double bonds.19,20 A number of calculational studies have examined various aspects of silicon-phosphorus bonding. Gordon and coworkers21 carried out HF/3-21G* calculations on SiPH5, SiPH3, and SiPH as prototypes of single, double, and triple SiP bonds. Cowley and collaborators22 studied various isomers of SiPH3 at the HF/6-31G** level of theory to explore the stability of SidP double bonds. Schleyer and Kost23 calculated the bond energy of H2SidPH in a comparison of double bond energies of second-row elements with carbon and silicon. Raghavachari (14) Baudler, M.; Scholz, G.; Tebbe, K.-F.; Feher, M. Angew. Chem., Int. Ed. Engl. 1989, 28, 339. (15) Walsh, R. The Chemistry of Organic Silicon Compounds; Patai, S., Rappoport, Z., Eds.; J. Wiley: New York, 1989; p 151. (16) Driess, M.; Gru¨tzmacher, H. Angew. Chem., Int. Ed. Engl. 1996, 35, 828. (17) Couret, C.; Escudie, J.; Satge, J.; Andriamizaka, J. D.; Saint-Roche, B. J. Organomet. Chem. 1979, 182, 9. (18) (a) Smith, C. N.; Bickelhaupt, F. Tetrahedron Lett. 1984, 25, 3011. (b) Smit, C. N.; Bickelhaupt, F. Organometallics 1987, 6, 1156. (c) van den Winkel, Y.; Bastiaans, H.; Bickelhaupt, F. J. Organomet. Chem. 1991, 405, 183. (d) Driess, M. Angew. Chem., Int. Ed. Engl. 1991, 30, 1022. (e) Driess, M.; Pritzkow, H. J. Chem. Soc., Chem. Commun. 1993, 1585. (19) Bender, H. R. G.; Niecke, E.; Nieger, M. J. Am. Chem. Soc. 1993, 115, 3314. (20) Driess, M.; Rell, S.; Pritzkow, H. J. Chem. Soc., Chem. Commun. 1995, 253. (21) Dykema, K. J.; Truong, T. N.; Gordon, M. S. J. Am. Chem. Soc. 1985, 107, 4535. (22) Lee, J.-G.; Boggs, J. E.; Cowley, A. H. J. Chem. Soc., Chem. Commun. 1985, 773. (23) Schleyer, P. v. R.; Kost, D. J. Am. Chem. Soc. 1988, 110, 2105.

© 1996 American Chemical Society

Silicon-Phosphorus Compounds et al.24 investigated the insertion of silylene into various species, including PH3. Maines et al.25 examined the 1,1-elimination of H2 from H3SiPH2 to form HSidPH2. A number of authors26 have calculated ring strain energies of heterosubstituted cyclopolysilanes and have noted that cyclic SiH2SiH2PH and other monosubstituted 3-membered polysilane rings have unusually short Si-Si bonds. Nyula´szi et al.27 have calculated HSiPH2 and H2SiPH in connection with a study of substituent effects on the stability of silylenes and silyl radicals. Schoeller and Busch28 have computed the cations, radicals, and anions of H2SiP and SiPH2. In the wake of recent experimental advances, Driess and Janoschek29 have also undertaken theoretical studies of H2SidPH and H2SidP-SiH3. The purpose of the present work is to expand our understanding of the structure and energetics of compounds with one or more SiP bonds. Specifically, we have used ab initio molecular orbital calculations at the MP2/6-31G* level of theory to determine the geometries and relative stabilities of various isomers of SiHmPHn (m + n ) 0-5) and SiHmPHnSiHo (m + n + o ) 0-7). Heats of formation and bond dissociation energies were then calculated for these isomers at the G2 level of theory,30 which has been shown to give reliable values that are within (2 kcal/mol of accurately known experimental energy differences.31 Methods Molecular orbital calculations were carried out with the GAUSSIAN 9432 series of programs using a variety of basis sets of split valence quality or better with multiple polarization and diffuse functions.33 Equilibrium geometries were optimized by Hartree-Fock and secondorder Møller-Plesset perturbation theory (HF/6-31G(d) and MP2(full)/ 6-31G(d), respectively) using a quasi-Newton optimization method.34 Vibrational frequencies and zero-point energies were calculated at the HF/6-31G(d) level using the HF-optimized geometries and analytical second derivatives.35 Thermal corrections to the energies were calculated by standard statistical thermodynamic methods using the HF/ (24) Raghavachari, K.; Chandrasekhar, J.; Gordon, M. S.; Dykema, K. J. J. Am. Chem. Soc. 1984, 106, 5853. (25) Maines, G. J.; Trachtman, M.; Bock, C. W. Theochem 1991, 231, 125. (26) (a) Grev, R. S.; Schaefer, H. F. J. Am. Chem. Soc. 1987, 109, 6577. (b) Cremer, D.; Gauss, J.; Cremer, E. Theochem 1988, 169, 531. (c) Boatz, J. A.; Gordon, M. S. J. Phys. Chem. 1989, 93, 3025. (27) Nyula´szi, L.; Belghazi, A.; Sze´tsi, S. K.; Veszpre´mi, T.; Heinicke, J. J. Mol. Struct. (Theochem) 1994, 313, 73. (28) Schoeller, W. W.; Busch, T. J. Mol. Struct. (Theochem) 1994, 313, 27. (29) Driess, M.; Janoschek, R. J. Mol. Struct. (Theochem) 1994, 313, 129. (30) (a) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221. (b) Curtiss, L. A.; Carpenter, J. E.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1992, 96, 9030. (31) Raghavachari, K.; Curtiss, L. A. In Modern Electronic Structure Theory Part II; Yarkony, D. R., Ed.; World Scientific Pub.: Singapore, 1995; p 991. (32) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A.; GAUSSIAN 94; Gaussian, Inc.: Pittsburgh, PA, 1995. (33) Hariharan, P. C.; Pople, J. A. Theor. Chem. Acta 1973, 28, 213 and references cited therein. Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265 and references cited therein. The 6-31G(d) and 6-31G(d,p) basis sets are the same as 6-31G* and 6-31G**, respectively. (34) Schlegel, H. B. J. Comput. Chem. 1982, 3, 214. Peng, C.; Ayala, P. Y.; Schlegel, H. B.; Frisch, M. J. J. Comput. Chem. 1996, 1, 49. (35) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem., Quantum Chem. Symp. 1979, 13, 225.

J. Am. Chem. Soc., Vol. 118, No. 35, 1996 8445 6-31G(d) frequencies. Correlated energies were calculated by fourthorder Møller-Plesset perturbation theory36 (MP4SDTQ, frozen core) and by quadratic configuration interaction with perturbative correction for triple excitations37 (QCISD(T), frozen core) with the MP2(full)/631G(d) optimized geometries. Atomization energies were computed by the G2 method,30 in which the energy computed at MP4/6-311G(d,p) is corrected for the effect of diffuse functions obtained at MP4/6-311+G(d,p), for the effect of higher polarization functions obtained at MP4/6-311G(2df,p), for the effect of electron correlation beyond fourth order obtained at QCISD(T)/6311G(d,p), and for the inclusion of additional polarization functions at MP2/6-311+G(3df,2p). Higher level corrections (HLC) for deficiencies in the wave function are estimated empirically30 by comparing the calculated and experimental bond dissociation energy for 55 wellcharacterized molecules. Most of the radicals have S2 in the range 0.75-0.80, but R-PdSiH, H2SiPSiH2, and cyclic HSiPSiH have somewhat larger spin contamination (1.1-1.3). Although energies computed with Møller-Plesset perturbation theory are significantly affected by spin contamination, energies calculated with the QCISD(T), CCSD(T), and G2 methods are not.30,38 Use of the spin-projected MPn energies in the G2 calculations instead of the unprojected values alters the G2 energies by less than 0.5 kcal/mol, even when there is significant spin contamination.

Results and Discussion The structures considered in the present work are shown in Figures 1-3. Total energies at the MP2(full)/6-31G*, QCISD(T)/6-311G**, G2MP2, and G2 levels, and harmonic vibrational frequencies calculated at the HF/6-31G* level for all of the structures are listed in the supporting information. Structures with the same number of hydrogen atoms are discussed as a group; within each group, structures are ordered approximately in terms of decreasing stability as calculated at the G2 level of theory. Structures, relative energies, and isodesmic reactions are considered first, followed by a discussion of the heats of formation and dissociation energetics. Unless otherwise stated, all energy differences discussed in the text are calculated at the G2 level of theory. Geometries and Relative Energies. (a) SiPH5. The MP2/ 6-31G* optimized geometry of silylphosphine, 1a, and the corresponding ylide, 1b, are in good agreement with previous calculations.20,27 The bond lengths in 1a are within 0.005 Å of the experimental values from the microwave structure;3 this suggests that a typical Si-P single bond length is ca. 2.25 Å. The ylide 1b is 34.3 kcal/mol less stable than silylphosphine, 1a, and has a significantly longer bond length (2.327 Å). By comparison, the corresponding carbon ylide,39 CH2PH3, is 45.9 kcal/mol higher than methyl phosphine and shows a 0.19 Å shortening of the C-P bond. (b) SiPH4. Two different isomers can be generated by removing a hydrogen from silylphosphine. Since the Si-H bond energy in SiH4 (91.3 kcal/mol) is greater than the P-H bond energy in PH3 (81.5 kcal/mol), it can be anticipated that structure 2b, SiH2PH2 (obtained by breaking an Si-H bond in SiH3PH2), is higher in energy than SiH3PH (obtained by breaking the P-H bond). The anti rotomer of SiH2PH2 is 1.5 kcal/mol lower than the gauche. For SiH3PH, two states need to be considered. The 2A′′ state, 2a, is 7.9 kcal/mol lower than 2b, has a normal Si-P single bond (2.254 Å), and has a small SiPH angle (93.4°, since the σ lone pair orbital on P is doubly (36) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618. (37) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (38) Chen, W.; Schlegel, H. B. J. Chem. Phys. 1994, 101, 5957. (39) G2 energies at 0 K for CH2PH3, propane, cyclopropane, and antiSiH3SiH2PH2 are -381.832856, -118.855804, -117.631143, and -923.186150 au, respectively.

8446 J. Am. Chem. Soc., Vol. 118, No. 35, 1996

Baboul and Schlegel

Figure 1. Equilibrium geometries for SiPHn optimized at the MP2(full)/6-31G(d) level of theory and relative energies of isomers computed at the G2 level of theory.

occupied). The 2A′ state is 38.6 kcal/mol higher than the 2A′′ state, has a short Si-P bond (2.194 Å, because of partial π bonding between phosphorus and silicon), and has a larger SiPH angle (127.8°, since the σ “lone pair” orbital is singly occupied). By comparison, the 2A1 state of PH2 is calculated to be 53.0 kcal/mol higher than the 2B1 state (experimental, 52.3 kcal/ mol40) and has a HPH angle of 121.2° (experimental, 123.2° 40). (c) SiPH3. Because this set of isomers contains the simplest example of a SidP double bond, it has been studied by a number of groups.20-22,27,29 Our findings are in good accord with previous results. The planar structure, 3a, has the lowest energy in this set. The SidP double bond length is 2.075 Å, in good agreement with the experimental value of 2.094 Å determined by X-ray crystallography on a sterically stabilized SidP double bond.19 An estimate of the π-bond energy of SidP can be obtained from the rotational barrier of H2SidPH, 28-34 kcal/ mol.29 Another estimate of the π-bond energy can be calculated from the following isodesmic reaction:23

SiH3 + PH2 + SiH3-PH2 f SiH2dPH + SiH4 + PH3

-37.9 kcal/mol

2SiH3 + SiH3-SiH3 f SiH2dSiH2 + 2SiH4

-32.7 kcal/mol41

Although the SiP π bond is a bit stronger than the SiSi π bond, the overall double bond strength for SidP is somewhat less than that of SidSi (e.g. 101 kcal/mol for SiH2dPH f 3SiH2 + 3PH42 vs 106 kcal/mol in SiH dSiH f 2 3SiH 41) because Si-P 2 2 2 (40) Berthou, J. M.; Pascat, B.; Guenebaut, H.; Ramsay, D. A. Can. J. Phys. 1972, 50, 2265.

σ bonds are weaker than Si-Si σ bond (e.g. 70 kcal/mol in SiH3PH2 versus 76 kcal/mol in SiH3SiH3). The next most stable structure is the silylene 3b, SiHPH2, which can be derived from SiH3PH2 by 1,1-elimination of H2. In keeping with the effect of electronegative substituents on silylenes, 3b is stabilized relative to unsubstituted silylene:44

SiH2 + SiH3SiH3 f SiH4 + SiH3SiH SiH2 + SiH3PH2 f SiH4 + SiHPH2 SiH2 + SiH3Cl f SiH4 + SiHCl

-0.7 kcal/mol -8.5 kcal/mol -9.8 kcal/mol46

Silylene 3b is only 14.3 kcal/mol higher than SiH2dPH, 3a. The phosphorus is significantly less pyramidal than usual (sum of the valence angles at P is 336.1°) and the barrier to inversion is very low;27 in addition, the Si-P bond length, 2.170 Å, is intermediate between typical single and double Si-P bonds (2.25 and 2.07 Å, respectively). These facts are consistent with a partial, dative π bond between the lone pair on P and the empty p orbital on Si that contributes to the ca. 8.5 kcal/mol stabilization of the silylene. (41) Curtiss, L. A.; Raghavachari, K.; Deutsch, P. W.; Pople, J. A. J. Chem. Phys. 1991, 95, 2433. (42) Homolytic cleavage of the double bond in SiH2dPH would yield two unpaired electrons on SiH2 (one from breaking the σ bond and one from breaking the π bond) and likewise two unpaired electrons on PH. Thus triplet SiH2 and triplet PH are the proper products if one is interested in the double bond strength. For further discussion see refs 43-45. (43) Janoschek, R. In Organosilicon Chemistry, from Molecules to Materials; Auner, N., Weis, J., Eds.; VCH Pub.: Weinheim, 1994; p 84. (44) Gordon, M. S.; Francisco, J. S.; Schlegel, H. B. AdV. Silicon Chem. 1993, 2, 137. (45) Grev, R. S. AdV. Organomet. Chem. 1991, 33, 125. (46) Su, M.-D.; Schlegel, H. B. J. Phys. Chem. 1993, 97, 8732.

Figure 2. Equilibrium geometries for Si2PHn optimized at the MP2(full)/6-31G(d) level of theory and relative energies of isomers computed at the G2 level of theory.

Silicon-Phosphorus Compounds J. Am. Chem. Soc., Vol. 118, No. 35, 1996 8447

8448 J. Am. Chem. Soc., Vol. 118, No. 35, 1996

Figure 3. Equilibrium geometry for (SiH3)3P optimized at the MP2(full)/6-31G(d) level of theory. (X is a dummy atom on the C3 axis.)

Structure 3c, SiH3P, is a ground state triplet with C3V symmetry that lies 21.4 kcal/mol higher than 3a. It has an typical Si-P single bond and can be derived from 1a by breaking two P-H bonds. Structure 3d, SiPH3, is also a ground state triplet and is 46.4 kcal/mol above 3a. (d) SiPH2. Compounds 4a, H2SidP, and 4b, SiHdPH, can be obtained by breaking an Si-H or P-H bond in H2SidPH; as expected, each structure is planar and has a Si-P double bond. The H2SidP isomer is 4.9 more stable than trans HSidPH which is 3.9 kcal/mol more stable than cis HSidPH. A different isomer, SidPH2 4c, is 9.0 kcal/mol higher than 4a; it has a nonplanar phosphorus (sum of valence angles at P is 339.8°) and an Si-P bond that is intermediate between a single and a double bond. It is analogous to silylene 3b, HSiPH2, and can be obtained from the latter by breaking a Si-H bond. (e) SiPH and SiP. Linear HSiP, 5b, has a SiP triple bond (1.984 Å), and by comparison with HCN, it would be expected to be the most stable isomer. However, Gordon and coworkers21 have previously shown that a hydrogen-bridged structure is lower in energy. This is reminiscent of Si2H2 which also has a bridged geometry.47 Bridged Si(H)P, 5a, has an SidP double bond, a PH single bond, and a partial SiH bond. At the G2 level of theory it is 10.4 kcal/mol more stable than HSitP. The diatomic SiP, 6, is a σ radical and has a triple bond with a length of 1.993 Å. The SiP triple bond appears to be ca. 40 kcal/mol stronger than the double bond, based on the following isodesmic reactions:

SiH3 + PH2 + SiH2dPH f HSitP + SiH4 + PH3

-35.3 kcal/mol

SiH3 + PH2 + SiHdPH f SitP + SiH4 + PH3

-47.2 kcal/mol

(f) Si2PH7. Disilylphosphine, 7, has geometrical parameters that are very similar to monosilylphosphine, 1a. The bond separation energy is small:

SiH3PHSiH3 + PH3 f 2SiH3PH2

2.8 kcal/mol

indicating relatively little interaction between the two Si-P bonds. By comparison with 1b the corresponding ylide is expected to be 30-40 kcal/mol higher in energy. The SiH3SiH2PH2 isomer39 is 4.9 kcal/mol higher than 7. (g) Si2PH6. Similar to SiPH4, the lowest energy Si2PH6 structure, 8a, is the 2B1 state resulting from breaking a P-H in Si2PH7; the 2A1 state is 29.1 kcal/mol higher. Cleavage of an (47) Colegrove, B. T.; Schaefer, H. F. J. Phys. Chem. 1990, 94, 5593. (48) Fanta, A. D.; Tan, R. P.; Comerlato, N. M.; Driess, M.; Powell, D. R.; West, R. Inorg. Chim. Acta 1992, 198-200, 733.

Baboul and Schlegel Si-H bond in Si2PH7 yields 8b, a structure that is 8.2 kcal/mol higher than 8a. This structure is the silyl-substituted analogue of 2b. The gauche rotomer is 0.9 kcal/mol higher than the anti rotomer. (h) Si2PH5. Of the structures considered, the phosphorusbridged, 3-membered-ring 9a has the lowest energy. The Si-P bond length is slightly longer than an average Si-P single bond (2.280 Å vs 2.25 Å), whereas the Si-Si bond length is intermediate between a single and a double bond (2.264 Å vs 2.335 Å in H3Si-SiH3 and 2.164 Å in H2SidSiH240). The shortening of Si-Si bonds in H2Si-X-SiH2 3-membered rings (X ) PH, S, NH, O) has been attributed to back-donation from X into the H2SidSiH2 π* orbital26a,b and to bond bending.26c Ring strain can be estimated by the following homodesmic reactions:

cyclic SiH2PHSiH2 + 2SiH3PH2 + SiH3SiH3 f 2SiH3SiH2PH2 + SiH3PHSiH3

-27.6 kcal/mol39

cyclic SiH2SiH2SiH2 + 3SiH3SiH3 f 3SiH3SiH2SiH3

-33.6 kcal/mol

cyclic CH2CH2CH2 + 3CH3CH3 f 3CH3CH2CH3

-27.4 kcal/mol39

The ring strain for cyclic Si3H6 is higher than that of cyclopropane because of increased bond bending strain and greater difficulty in forming suitable hybrid orbitals at silicon.26b,c The decrease in ring strain in going from cyclic Si3H6 to cyclic Si2PH5 is due to a decrease in angular strain because of the smaller valence angles at phosphorus.26b West and co-workers48 have tentatively identified a substituted example of 3-memberedring 9a as an intermediate in the reaction of P4 with disilenes. The acyclic compound with a double bond, SiH3PdSiH2 9b, is only 2.0 kcal/mol higher than the cyclic structure, 9a. The π-bond energy is very similar to SiH2dPH:

SiH3 + PH2 + SiH3-PH-SiH3 f SiH3-PdSiH2 + SiH4 + PH3

-39.6 kcal/mol

Driess et al.18d have recently synthesized a sterically stabilized R2SidP-SiR′3, where R and R′ are large, bulky groups. They have also compared observed and calculated properties for R2SidXR and R2SidPSiR3.29 The calculated geometry of 9b is essentially H2SidPH, 3a, substituted by a silyl group; the structure shows little specific interaction between the Si-P single and double bonds. The silylene isomer, anti SiH3PHSiH 9c, and its syn conformer are silyl-substituted analogues of 3b and are 13.8 and 14.9 kcal/mol higher than 9b. Each of these silylenes has a remarkably small HSiP angle (less than 90°), a 0.02-0.03 Å shortening of both the SiP bonds, and a flattening of the pyramidal P, indicating some interaction between the silyl group and the H2SidP moiety. This is confirmed by examining the appropriate bond separation reaction:

SiH3PHSiH + PH3 f SiH3PH2 + SiHPH2

4.9 kcal/mol

(i) Si2PH4. The lowest energy structure is the 2B1 state of the 3-membered-ring 10a. It can be obtained by breaking the P-H bond in the 3-membered-ring 9a and shows even more shortening of the Si-Si bond than the latter. The 2A1 state is a ca. 10 kcal/mol less stable than the 2B1 state. The other 3-membered ring, 10b, is 7.2 kcal/mol higher than 10a. The

Silicon-Phosphorus Compounds

J. Am. Chem. Soc., Vol. 118, No. 35, 1996 8449

ring strain in these structures is similar to cyclic Si2PH5, 9a, as computed by the following isodesmic reactions:

silylene and there is a sizable interaction between the two SiP bonds:

cyclic SiH2PSiH2 + 2SiH4 f SiH3PSiH3 + SiH3SiH3

-23.5 kcal/mol

SiH2dP-SiH + PH3 f SiH2dPH + SiH-PH2

cyclic SiH2PHSiH + 2SiH4 f SiH3PHSiH2 + SiH3SiH3

-22.5 kcal/mol

cyclic SiH2PHSiH2 + 2SiH4 f SiH3PHSiH3 + SiH3SiH3

-24.6 kcal/mol

The most stable acylic structure is trans H3SiPHdSiH, 10c, which is 6.8 kcal/mol higher than 10a. The cis isomer of H3SiPHdSiH is 2.8 kcal/mol less stable than the trans. Structure 10d, SiH3PHSi, is 10.9 kcal/mol above 10a and is the silyl-substituted analogue of H2PSi, 4a; both SiP bonds in 10d show ca. 0.02 Å shortening, indicating some interaction between the bonds:

SiH3PHSi + PH3 f SiH3PH2 + SiPH2

5.1 kcal/mol

Breaking the Si-Si bond and opening the 3-membered ring in 10a is endothermic by only 10.5 kcal/mol (however, there is probably a significant barrier); the resulting species, 10e, is isoelectronic with allyl radical and the SiP bond lengths are intermediate between single and double bonds. From the following isodesmic reaction,

2SiH3 + PH2 + SiH3PHSiH3 f SiH2PSiH2 + 2SiH4 + PH3

-43.0 kcal/mol

one can see that the strength of the allylic π bond is slightly greater than π-bond energy of the double bond in SiH2dPH. Structures 10f and its syn isomer can be obtained by Si-Si bond cleavage and ring opening of 10b (endothermic by 16.2 and 18.1 kcal/mol, respectively). In both of these isomers, the PdSiH fragments resemble 3b, although the P is less pyramidal; the H2Si-P fragments resemble 2b, but the Si-P bond is somewhat shorter, indicating a small interaction with the neighboring SidP. (j) Si2PH3. Three different cyclic species can be constructed. Structure 11a is the most stable and has a somewhat elongated Si-P single bond and SidP double bond, but an SiSi bond that is almost as short as H2SidSiH2. The SidP π-bond energy, as estimated by the following isodesmic reaction,

SiH3 + PH2 + cyclic SiH2-PH-SiH2 f cyclic SiH2-PdSiH + SiH4 + PH3

-40.4 kcal/mol

is similar to acyclic SidP double bonds in 3a and 9b (-37.9 and -39.6 kcal/mol, respectively). Silylene 11b is 7.9 kcal/ mol higher than 11a and can be obtained by 1,1-H2 elimination from 9a. The SiSi bond is normal, but the SiP bonds are 0.050.06 Å shorter than normal. The ring strain in 11b is somewhat less than in 9a because of the smaller valence angle of silylenes:

cyclic SiH2PHSi + 2SiH4 f SiH3PHSiH + SiH3SiH3

-17.8 kcal/mol

Structure 11c with an SidSi double bond is a transition state for PH migration. The acyclic isomer 11d has an SiP single bond and an SiP double bond. This structure is 16.3 kcal/mol above 11a and can be generated from 9b by 1,1-elimination of H2 to give a silylene or by breaking the SiSi doble bond in 11a. The geometry of 11d resembles 3a substituted with a

7.0 kcal/mol

Compound anti,anti-11e, the syn,anti isomer, and the syn,syn isomer have π systems that are isoelectronic with allyl cation and the Si-P bonds show the requisite shortening. The structures are 25.6, 26.4, and 27.3 kcal/mol above 11a, respectively. (k) Si2PH2. Isomer 12a is the most stable and can be obtained from 10a by 1,1-elimination of H2 or from 11b by PH bond cleavage. There is considerable shortening of the SiP bond to give it nearly double bond character. The other two cyclic structures, 12b and 12c, are significantly higher in energy (21.0 and 25.2 kcal/mol, respectively). In both cases there is a partial multiple bond in the ring. Acyclic isomers HSiPSiH and HSiPHSi were also considered, but were found to be significantly less stable than the cyclic structures. (l) Si2PH and Si2P. The three-membered ring with an Si-H bond, 13a, is 11.2 kcal/mol more stable than the isomer with a P-H bond, 13b. The 2A1 state is the most stable state for Si2P, 14; the 2B2 state is 19.8 kcal/mol higher. Structure 13a has an SiP single bond while 13b and 14 have SiSi single bonds; the other ring bonds have partial double bond character. (m) Si3PH9. Trisilylphosphine, 15, is a pyramidal with the silyl groups in a staggered conformation. At the Hartree-Fock level, the symmetry is C3V, but at the MP2/6-31G(d) level the silyl groups twist by ca. 10° to yield an equilibrium structure with C3 symmetry. Because there are 3 pairs of Si-P bond interactions, the bond separation energy for Si3PH9 is approximately 3 times the bond separation energy for Si2PH7:

(SiH3)3P + 2PH3 f 3SiH3PH2

9.8 kcal/mol

Heats of Formation, Bond Energies, and Decomposition Reactions. The G2 energies (listed in the supporting information) were used to calculate the atomization energies listed in Table 1. These were then combined with the gas-phase heats of formation of the atoms to give the heats of formation of the molecules under discussion. While the heats of formation of hydrogen and phosphorus atoms are known very well49 (52.10 and 75.62 kcal/mol, respectively, at 298 K, 1 atm), there is a bit of uncertainty for silicon. Grev and Schaefer50 and Ochterski, Petersson, and Wiberg51 have recently suggested the value listed in the JANAF tables,47 107.55 ( 2 kcal/mol (at 298 K), is too low based on a comparison between very high level calculations and the experimental heat of atomization of silane and disilane. We have used their recommendation50,51 of 108.1 ( 0.5 kcal/mol at 0 K or 109.1 kcal/mol at 298 K. For a series of 125 energy differences whose experimental values are known accurately, the mean absolute error in the values calculated at the G2 level of theory is 1.3 kcal/mol.30,31 The accuracy and reliability of calculated heats of formation listed in Table 1 should be similar. For the molecules in the present study, the mean absolute difference in atomization energies computed at the G2 and G2(MP2) levels of theory is 0.5 kcal/mol (G2(MP2) results are available in the supporting information). Table 2 presents the dissociation enthalpies for the weakest bonds in the compounds considered. Simple Si-H, P-H, and (49) Chase, M. W.; Davies, C. A.; Downey, J. R.; Frurip, D. J.; McDonald, R. A.; Szverud, A. N. JANAF Thermochemical Tables, 3rd ed. In J. Phys. Chem. Ref. Data 1985, 14. (50) Grev, R. S.; Schaefer, H. F. J. Chem. Phys. 1992, 97, 8389. (51) Ochterski, J. W.; Petersson, G. A.; Wiberg, K. B. J. Am. Chem. Soc. 1995, 117, 11299.

8450 J. Am. Chem. Soc., Vol. 118, No. 35, 1996

Baboul and Schlegel

Table 1. Atomization Energies, Heats of Formation, and Entropies for SiPHn, Si2PHn, and Si3PH9 Computed at the G2 Level of Theorya structure 1a 1b 2a 2b 3a 3b 3c 3d 4a 4b 4c 5a 5b 6 7 8a 8b 9a 9b 9c 10a 10b 10c 10d 10e 10f 11a 11b 11d 11e 12a 12b 12c 13a 13b 14 15

H3Si-PH2 H2Si-PH3 H3Si-PH 2A′′ H2Si-PH2 anti H2SidPH HSi-PH2 H3Si-P Si-PH3 H2SidP HSidPH trans Si-PH2 Si(H)P HSitP SitP H3Si-PH-SiH3 H3Si-P-SiH3 2B1 H3Si-PH-SiH2 anti H2Si-PH-SiH2 c H3Si-PdSiH2 H3Si-PH-SiH anti H2Si-P-SiH2 c 2B1 H2Si-PH-SiH c H3Si-PdSiH trans H3Si-PH-Si H2Si-P-SiH2 H2Si-PHdSiH anti H2Si-P-SiH c H2Si-PH-Si c H2SidP-SiH anti,anti HSi-PH-SiH H2Si-P-Si c HSi-PH-Si c HSi-P-SiH c HSi-P-Si c Si-PH-Si c Si-P-Si c 2A1 (SiH3)3P

Table 2. Energies for Unimolecular Decomposition Computed at the G2 Level of Theorya bond breakingb

sym- atomization heat of metry energy formation entropy Cs Cs Cs Cs Cs C1 C3V C3V Cs Cs Cs Cs C∞V C∞V Cs C2 C1 Cs Cs C1 C2V C1 Cs C1 C2 C1 Cs C1 Cs C2V Cs C1 C2 Cs C2V C2V C3

428.5 394.2 347.5 339.6 293.5 279.2 272.1 247.1 213.7 208.8 204.7 166.4 156.0 83.1 633.3 552.9 544.7 502.0 500.1 486.2 422.7 415.6 416.0 411.8 412.2 399.4 369.6 361.8 353.3 344.1 300.8 279.8 275.6 247.4 236.2 183.1 842.5

9.7 44.2 40.0 47.9 42.9 57.4 64.3 89.5 72.1 76.9 80.9 68.8 79.0 100.8 15.1 44.8 53.0 44.2 46.5 60.5 72.8 79.9 80.0 84.1 83.9 96.7 74.9 83.1 91.8 101.2 93.2 114.2 118.4 95.7 107.0 109.2 16.5

66.1 67.6 66.8 66.9 62.0 63.3 62.4 64.1 63.0 62.8 63.1 61.6 56.0 54.8 80.2 83.1 80.9 71.7 75.5 77.4 72.5 72.4 78.1 77.5 77.0 77.2 69.2 71.0 73.3 77.5 71.4 71.3 70.9 67.7 69.2 67.1 92.5

a

G2 atomization energies in kcal/mol at 0 K, heats of formation in kcal/mol at 298 K, entropies in cal/deg mol at 298 K; cyclic molecules are designated by the suffic c.

Si-P bond cleavage in saturated compounds requires 70-90 kcal/mol. The strength of an SidP double bond, 77-80 kcal/ mol, is only about 10% greater than a normal single bond strength, 70-76 kcal/mol, based on singlet silylene as a product. If one uses triplet SiH2,42 the SidP double bond is ca. 30 kcal/ mol stronger than the single bond. Likewise, if quartet SiH is used, the SiP triple bond is ca. 50-60 kcal/mol stronger than the single bond. Lower values for bond strengths in some of the compounds are due to unstable reactants or particularly stable products. For example, Si-H breaking in 2a, 8a, and 10a and P-H breaking in 2b, 8b, and 10b are 45-55 kcal/mol because of the formation of an SidP double bond. Formation of silylenes also leads to low Si-H bond energies in 2b, 4a, 8b, and 10e. The Si-P bond energies in 1b, 3d, and 10d are only 20-32 kcal/mol because the reactants are relatively unstable. Note, however, that there may be significant barriers associated with some of the bond-breaking processes that involve rearrangement of bonding. Other important routes for the decomposition of silicon compounds are the 1,1-elimination of H2 and silylene-elimination reactions. The heats of reaction for some of these processes that can be computed from the present data are also listed in Table 2. Of the reactions listed, only SiH3PH2 f SiH2 + PH3 and SiH3PH2 f SiHPH2 + H2 have been studied previously.24,25 Typically, silylene insertions and additions have very low barriers. Hence, the barriers for H2 and SiH2 elimination will

structure 1a 1b 2a 2b 3a 3b 3c 3d 4a 4b 4c 5a 5b 6 7 8a 8b 9a 9b 9c 9d 10a 10b 10c 10d 10e 10f 11a 11b 11d 11e 12a 12b 12c 13a 13b 15

H3Si-PH2 H2SiPH3 H3Si-PH H2Si-PH2 H2SidPH HSi-PH2 H3Si-P Si-PH3 H2SidP HSidPH Si-PH2 Si(H)P HSitP SitP H3Si-PH-SiH3 H3Si-P-SiH3 H3Si-PH-SiH2 H2Si-PH-SiH2 c H3Si-PdSiH2 H3Si-PH-SiH H3Si-PH-SiH H2Si-P-SiH2 c H2Si-PH-SiH c H3Si-PdSiH H3Si-PH-Si H2Si-P-SiH2 H2Si-PHdSiH H2Si-P-SiH c H2Si-PH-Si c H2SidP-SiH HSi-PH-SiH H2Si-P-Si c HSi-PH-Si c HSi-P-SiH c HSi-P-Si c Si-PH-Si c (SiH3)3P

SiH

PH

SiP

elimination SiSi

H2

SiH2

88.9 81.0 54.6 54.0 75.4 60.4 46.1 84.7 79.8 74.6 70.4 58.5 42.5 57.7 42.4 52.8 38.2 83.3 72.9

70.1 45.0 54.9 20.7 -3.5 64.8 34.5 55.5 47.6 21.7 77.2 (100.6) 22.9 63.6 19.0 58.6 55.9 20.7 66.6 (89.9) 26.3 68.9 59.8 17.3 97.3 85.3 (126.6) 83.1 88.6 80.4 72.3 42.9 57.7 52.8 67.2 32.7 59.1 42.7 44.6 37.6 42.5 58.0 86.5 80.4 15.8 36.1 61.4 84.1 72.9 42.6 59.4 74.4 70.3 63.9 38.0 59.9 73.4 69.2 62.9 36.9 58.8 53.1 6.8 17.7 61.9 53.8 45.9 17.6 31.5 59.6 62.6 46.4 60.0 50.1 31.9 60.0 58.9 51.4 55.3 46.0 43.4 68.8 16.3 18.0 66.5 81.9 60.9 21.3 48.2 52.5 68.9 64.3 68.5 64.5 53.4 32.7 70.6 43.6 32.4 28.2 83.5 72.3 76.0 62.0

a In kcal/mol at 0 K for breaking the weakest bond; cyclic molecules are designated by the suffix c. b Values in parentheses are calculated using triplet SiH2 and quartet SiH; these are appropriate for determining the SiP double and triple bond strength.42

be only a bit higher than the heats of reaction listed in the table (by contrast, 1,2-elimination of H2 can have rather high barriers52). Some of the more facile decomposition reactions include H2 elimination from 2b, 3a, 3b, 4d, 10a, 11a, and 11b. In each case the product is stabilized by the formation of a multiple bond. The heats of reaction for SiH2 elimination are typically 10-20 kcal/mol higher than 1,1-elimination of H2. A bond additivity scheme53 can be constructed to fit the calculated atomization energies in Table 1 and related data for SiHn, Si2Hn, Si3H8,41 and PHn. Because of the special nature of their bonding, ylides H2SiPH3 and SiPH3 and partial aromatic 3-membered rings 13a, 13b, and 14 were not included. Note that the average bond energies used for the additivity scheme are not the same as the dissociation energies (kcal/mol) for specific bonds in individual compounds: Si-H ) 73.5 Si-Si ) 55 Si-P ) 55 3-membered ring ) -30

P-H ) 73 SidSi ) 57 SidP ) 69

SitSi ) 71 SitP ) 86

These average bond energies yield an estimated mean absolute deviation of 5.3 kcal/mol in the atomization energies. The major (52) Gordon, M. S.; Truong, T. N.; Bonderson, E. K. J. Am. Chem. Soc. 1986, 108, 1421. (53) Cohen, N.; Benson, S. W. Chem. ReV. 1993, 93, 2419.

Silicon-Phosphorus Compounds errors in the bond additivity scheme are due to the stability of silylenes, dative bonding, and conjugation. The ring strain term was needed for a reasonable fit, but further refinement is probably not warranted for the size of the database. A group additivity scheme53 can give a significantly better fit to the atomization energy: 92 kcal/mol for Si with 4 single bonds 68 kcal/mol for Si with 1 double bond and 2 single bonds 56 kcal/mol for Si with 1 triple bond and 1 single bond 56 kcal/mol for Si with 3 single bonds 44 kcal/mol for Si with 1 double bond and 1 single bond 37 kcal/mol for Si with 1 triple bond 41 kcal/mol for singlet Si with 2 single bonds 17 kcal/mol for triplet Si with 2 single bonds 37 kcal/mol for Si with 1 double bond 17 kcal/mol for Si with 1 single bond 72 kcal/mol for P with 3 or 4 single bonds 65 kcal/mol for P with 1 double bond and 1 single bond 46 kcal/mol for P with 1 triple bond 43 kcal/mol for P with 2 single bonds or 1 double bond 18 kcal/mol for triplet P with 1 single bond 53.3 kcal/mol for terminal H, 60 kcal/mol for bridging H -14 kcal/mol for 3-membered rings 14 kcal/mol for each dative bond 35 kcal/mol for allylic π conjugation in an Si-P-Si group

For 18 compounds in the series for SiHn, Si2Hn, and Si3H8 the mean absolute deviation is 1.3 kcal/mol in the atomization energies. For the entire set of SiPHn, Si2PHn, Si3PH9, SiHn, Si2Hn, Si3H8, and PHn (58 compounds), the mean absolute deviation is 3.4 kcal/mol. Special terms for ring strain, dative bonding (e.g structures 3b, 4c, 9c, 10d, 10f, etc)., and allylic conjugation (structures 10e, 11e, 12c, 13a, 13b, and 14) were required for a good fit. This scheme should to be a useful start for approximating the energies of larger systems. As more data become available, the group contributions will need to be extended to a larger set of groups with more specific bonding. Another method for estimating the energies involves isodesmic reactions (reactions that conserve the numbers of each type of bond). For example, the atomization energies of acyclic Si2PHn can be approximated from the energies of SiPHn using the reaction:

J. Am. Chem. Soc., Vol. 118, No. 35, 1996 8451

SiHmPHa + SiHnPHb f SiHmPH3-a-bSiHn + PH3 For perfect additivity of bond energies, the reaction enthalpy would be zero. For 12 acyclic Si2PHn, the average reaction energy is 5.7 kcal/mol, indicating a significant 1,3-interaction. The average deviation, however, is only 1.7 kcal/mol indicating that the 1,3-interaction is fairly constant and that the estimated energies are much less variable than the bond or group additivity methods. Furthermore, isodesmic reaction energies can be computed quite reliably at fairly low levels of theory (e.g. MP2/ 6-31G(d)). Thus, the SiPHn and Si2PHn energies in the present work can be used as templates to estimate the energies of larger systems using isodesmic reactions. Summary The present study examined a total of 48 isomers and states of silicon-phosphorus compounds at the G2 level of theory. There are a number of examples of Si-P double bonds. Silylenes and cyclic compounds are also abundant for structures with low numbers of hydrogens. Some of these are stabilized by dative bonding and allylic conjugation. Structure 9b is the parent of a sterically stabilized compound synthesized by Driess.18 Compounds based on 3-membered-ring 9a and possibly silylene 9c are also interesting candidates for synthesis because of their structure and stability. Other molecules that might be considered include unsaturated rings, 11a and 11b, and species with allylic conjugation, 11e and 10e. The calculated heats of formation provide a guide to the relative energies and stabilities of the various isomers. Simple bond additivity and group additivity schemes have been developed for estimating the energies of larger systems. Acknowledgment. This work was supported by a grant from the National Science Foundation (CHE 9400678). We would like to thank the Pittsburgh Supercomputing Center for computer time. Supporting Information Available: Total energies at the MP2(full)/6-31G(d), QCISD(T)/6-311G(d,p), G2(MP2), and G2 levels of theory, and harmonic vibrational frequencies at the HF/6-31G(d) level for all structures (4 pages). See any current masthead page for ordering and Internet access instructions. JA960771W